VSE/Compositor - Something similar to Turbulence Displacement effect in After Effects
Try a Displace node with a Clouds procedural texture (in the compositor):




The nodes in the "X Y scale" frame are just for convenience, you can also set the scale directly on the texture node. 
The mix node in the "Recenter" frame subtracts .5 gray to keep the result in place; the displace node moves pixels up/right for positive numbers and down/left for negative numbers. To move pixels both ways, the 0..1 range of the texture needs to be shifted to -.5..+.5.


The scale inputs on the displace node itself set the distance (in pixels) a value of 1 in the vector input will move the corresponding pixel of the image input. In this example I set the vertical scale to 0 to mimic your reference image.